Properties

Label 39.2.b
Level $39$
Weight $2$
Character orbit 39.b
Rep. character $\chi_{39}(25,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $9$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 39.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(39, [\chi])\).

Total New Old
Modular forms 6 2 4
Cusp forms 2 2 0
Eisenstein series 4 0 4

Trace form

\( 2q - 2q^{3} - 2q^{4} + 2q^{9} + O(q^{10}) \) \( 2q - 2q^{3} - 2q^{4} + 2q^{9} + 2q^{12} - 2q^{13} + 12q^{14} - 10q^{16} - 12q^{17} + 12q^{22} + 10q^{25} - 12q^{26} - 2q^{27} + 12q^{29} - 2q^{36} - 12q^{38} + 2q^{39} - 12q^{42} - 8q^{43} + 10q^{48} - 10q^{49} + 12q^{51} + 2q^{52} + 12q^{53} + 12q^{56} - 4q^{61} + 12q^{62} - 2q^{64} - 12q^{66} + 12q^{68} - 24q^{74} - 10q^{75} - 24q^{77} + 12q^{78} - 16q^{79} + 2q^{81} + 24q^{82} - 12q^{87} + 12q^{88} + 24q^{91} - 12q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(39, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
39.2.b.a \(2\) \(0.311\) \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-\zeta_{6}q^{2}-q^{3}-q^{4}+\zeta_{6}q^{6}+2\zeta_{6}q^{7}+\cdots\)